As a social science, contemporary political science started to take shape in the latter half of the 19th century. At that time it began to separate itself from political philosophy, which traces its roots back to the works of Chanakya, Aristotle, and Plato which were written nearly 2,500 years ago. The term "political science" was not always distinguished from political philosophy, and the modern discipline has a clear set of antecedents including also moral philosophy, political economy, political theology, history, and other fields concerned with normative determinations of what ought to be and with deducing the characteristics and functions of the ideal state.

When did political science become an academic discipline? Let's have some stream of consciousness first.
The relevant sentence in the passage is: As a social science, contemporary political science started to take shape in the latter half of the 19th century. So, the answer is the latter half of the 19th century.